README.md

LBP-Reformulation

This is a Python framework to reformulate a class of linear bilevel programs (LBP) to (one-level) nonlinear programs, and solve the latter using a nonlinear solver such as baron.

$$ \begin{equation}\tag{LBP} \min_{x\in\mathbb{R}^n, y\in\mathbb{R}^q}{\langle c,x\rangle+\langle d,y\rangle}\quad\text{s.t.}\quad \begin{cases} Ax=b\\ x\geq0\\ y\geq0\\ y\in arg\min_{y'\geq0}{{\langle e,x\rangle+\langle f,y'\rangle|Cy'=a-Bx}} \end{cases} \end{equation} $$

To run the project, the AMPL executable's path should be in the system PATH. We use python

To run the project with test instances:
python3 blevp2nlp.py -t

To run the project with an AMPL-formatted ".dat" file:
python3 blevp2nlp.py -d [path to '.dat' file]

For instance:
python3 blevp2nlp.py -d tests/test_pb_4.dat

Solver statuses according to the AMPL book:

Message	Interpretation
solved	optimal solution found
solved?	optimal solution indicated, but error likely
infeasible	constraints cannot be satisfied
unbounded	objective can be improved without limit
limit	stopped by a limit that you set (such as on iterations)
failure	stopped by an error condition in the solver